Brownian Particles with Rank‐Dependent Drifts: Out‐of‐Equilibrium Behavior
Brownian Particles with Rank‐Dependent Drifts: Out‐of‐Equilibrium Behavior
Abstract We study the long‐range asymptotic behavior for an out‐of‐equilibrium, countable, one‐dimensional system of Brownian particles interacting through their rank‐dependent drifts. Focusing on the semi‐infinite case, where only the leftmost particle gets a constant drift to the right, we derive and solve the corresponding one‐sided Stefan (free‐boundary) equations. Via this …